The ability of households to smooth consumption and firms to invest depends on O their objective function. their ability to borrow (or save). whether share prices are rising. whether the assumption of rationality holds.
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- Assume a consumer has current-period income y = 200, future-period income y′ = 150, current and future taxes t = 40 and t′ = 50, respectively, and faces a market real interest rate of r = 0.05, or 5% per period. The consumer would like to consume according to the following utility function: U (c, c′ ) = ln(c) + ln(c′ ). Show mathematically the lifetime budget constraint for this consumer. Find the optimal consumption in the current and future periods and optimal saving. Suppose that instead of r = 0.05 the interest rate is r = 0.1. Repeat parts (a) and (b). Does the substitution effect or the income effect dominate?Consider an individual who lives for two periods and has utility of lifetime consumption U = log(C1) + 1/1+δ log(C2), where C1 and C2 are the consumption levels in the first and second period respectively, and δ, 0 1 > 0 in the first period and no income in the second period, so Y2 = 0. He can transfer some income to the second period at a before-tax rate of return of r, so saving $S in the first period gives $[1 + r]S in the second period. The government levies a capital tax at rate τ on capital income received in the second period. The tax proceeds are paid as a lump-sum transfer to the following generation. The present generation does not care about the next one. a. What is the lifetime consumption profile of this individual? What is his lifetime indirect utility function expressed as a function of Y1 and b. Evaluate the change in initial income Y1 that is required to compensate the individual for the welfare loss due to the capital income tax τ. c. What is…please solve it completely. Bob has preferences over consumption in period 0 and 1 of the form U(x, y) = xy, where x and y are Bob's consumption in period 0 and 1 respectively. He has $15,000 in the bank now and is trying to decide between two different investment opportunities, A and B. A: invest $10,000 in period 0 and receive $20,000 in period 1. B: invest $2,000 in period 0 and receive $6,000 in period 1. If Bob can borrow and lend at a rate of interest of 50 percent, which investment opportunity will he choose? Given your answer in (a), how much will he consume in each period if the price of the good is $1 in both periods? Given your answer in (a), how much will he consume in each period if the price in period 0 is $1 and the inflation is 20%? Assuming that the price of consumption is $1 in both periods and the borrowing rate is 50% and the lending rate is 100%. Given your answer in (a), how much will he consume in each period?
- Suppose that firms produce according to the production function Y = AK1/2L1/2, where A = 5 andL = 400. Assume that the prices of capital and output are equal and that the real interest rate, r, isequal to 0.25 and the depreciation rate, δ, is equal to 0.1.1. If firms operate according to the neoclassical theory of investment, what is the optimal levelof capital stock, K (YP) to rich (YR).22. Suppose that the government offers an investment tax credit which changes the relative priceof capital. This results in Pk = 3 and P = 6. What is the new optimal level of capital stock,K??3. Does the investment tax credit have an expansionary impact on the economy? Explain whyor why not.4. Based on the optimal capital stock computed in part (2), what is the level of investmentneeded to sustain this level of capital stock?Suppose that a consumer/investor has an initial endowment only for the current period, which is Eo =450. She may consume today or in the next period only (two-period model). The interest rate for borrowing and lending in the capital market is 5% (a)Depict the budget constraint for the investor in an inter-temporal consumption diagram! What is the maximum amount the consumer is able to consume in the next period? (b)The consumption preferences of the consumer/investor are best described by a square root function, defined over current and future consumption. What is his optimal consumption plan? Show your calculations! Depict the results in appropriate diagram. Which amount is invested in the capital market?Consider an economy where individuals live for two periods only. Their utility function over consumption in periods 1 and 2 is given by U = 2 log(C1) + 2 log(C2), where C1 and C2 are period 1 and period 2 consumption levels respectively. They have labor income of $100 in period 1 and labor income of $50 in period 2. They can save as much of their income in period 1 as they like in bank accounts, earning interest rate of 5 percent per period. They have no bequest motive, so they spend all their income before the end of period 2. a. What is each individual’s lifetime budget constraint? If they choose consumption in each period so as to maximize their lifetime utility subject to their lifetime budget constraint, what is the optimal consumption in each period? How much do the consumers save in the first period? b. Suppose that the government introduces a social security system that will take $10 from each individual in period 1, put it in a bank account, and transfer it back to…
- a) Draw a consumption function and label the axes.b) Suppose that your friend has a consumption function of the form y=1.4x+200. Is this function sustainable in the long run? Why or why not?c) Suppose that your consumption function is y=0.75+1000. What is your marginal propensity to consume? What is your autonomous expenditure?d) State the permanent income hypothesis.e) Suppose that I raise your income today by $10, and lower it tomorrow by $10. How would your behavior change according to the consumption function (aka Keynesian, aka rule-of-thumb) model? And what about according to the permanent income hypothesis model?Please no written by hand solutions Data on before-tax income, taxes paid and consumption spending (on domestic goods and services) for the Simpson family in various years are given below. BEFORE-TAX INCOME ($) TAX PAID ($) CONSUMPTION SPENDING ($) 3000 3500 3700 4000 25 000 27 000 28 000 30 000 20 000 21 350 22 070 23 600 a. Graph the Simpsons's consumption function and find their household's marginal propensity to consume. b. How much would you expect the Simpsons to consume if their income was $32 000 and they paid taxes of $5000? c. Homer Simpson wins a lottery prize. As a result, the Simpson family increases its consumption by $1000 at each level of after-tax income. ('Income' does not include the prize money.) How does this change affect the graph of their consumption function? How does it affect their marginal propensity to consume?A consumer's current income (y) is 200 and the future income ( t.') is 240. A current lump sum tax (t) of 10 is paid and the tax in the next period (t) is 15. The real interest rate is 20% for each period. Please assume that current and future consumption are complements. and the consumer always prefers to have one unit of current consumption and two units of consumption in the future. Calculate the optimal current and future consumption and the optimal current and future savings. Is the consumer a lender or a borrower? How does he she. as a lender or a borrower. affect the future consumption?
- A decision maker allocates an endowment of W > 0 dollars across two periodst = 1, 2. He discounts the future by β ∈ (0, 1) while facing a gross interest rateof R > 1. His utility is the same as studied in class. Solve for the intertemporalchoice problem. Show that the optimal consumption is decreasing over time ifβR < 1, constant over time if βR = 1, and increasing over time if βR > 1.Assumptions for all the questions: Private consumption is a function of disposable income and wealth (unless stated otherwise). Investment depends only on the real interest rate (unless stated otherwise). please present your answer using graphs and short explanations. Assume that the economy is open and that CF= 0. Assume that Y*< Yfull. Analyze the influence of the following events (analyze each event separately unless said otherwise) on the equlibrium outcomes. Use the diagrams and show the changes relative to the initial situation which you described in A. In each section show what will happen to output, real interest rate, net capital flow (CF), import surplus (IM-EX), real exchange rate, private consumption, investment and inflation rate in the short run and in the long run. a) Assume that we are in the initial situation of short-run equilibrium described above. The government decided to decrease taxes and increase bonds in order to increse household consumption. asume…Suppose a consumer has $1500 in the current time period and $1100 in the future time period.Suppose also that the consumer can borrow and lend freely and, unless otherwise specified, borrowing and lending interest rates are the same. (a) If the interest rate between time periods is 50%, what is the budget constraint between consumption in the present and consumption in the future? (B) If the interest rate at which the consumer can borrow is 75% but the rate at which she can lend is25%, what is the budget constraint? (C) Suppose the interest rate is 50%. If the consumer has to pay a fee of 10% of the loan amount in order to borrow money, what is the budget constraint?